1. Field
The following relates to approaches for adaptive sampling in ray tracing and more particularly to approaches to progressive refinement of images produced using statistical sampling techniques.
2. Related Art
Rendering images from 3-D scenes using ray tracing is based on the theory of evaluating a rendering equation, which includes a number of nested integrals that model different light behaviors and which is difficult to solve analytically. Therefore, approximations for solving the rendering equation have been developed. One successful set of approaches to approximating the rendering equation is to use sampling techniques. The integral is evaluated at a number of discrete values, which can be determined randomly, to produce a probabilistic estimate of the integral from the samples.
These procedures are referred to as Monte Carlo integration. An integral F=∫f(x)dx can be estimated using Monte Carlo integration as
  F  ≈            1      n        ⁢                  ∑                  i          =          1                n            ⁢                        f          ⁡                      (                          X              i                        )                                    p          ⁡                      (                          X              i                        )                              where x is determined according to a random variable X, distributed according to probability density function p(x). The mathematics shows that so long as the sampling is performed correctly, the estimate eventually will converge to a correct result. A principal issue arising in Monte Carlo integration is getting acceptable accuracy with a reasonable or limited number of samples. Having too few samples results in an excessively noisy image and taking additional samples of pixels that have actually converged is wasteful.